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The Journal of Neuroscience, July 23, 2003, 23(16):6499-6509
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Vibrissa Resonance as a Transduction Mechanism for Tactile Encoding
Maria A. Neimark,1 * Mark L. Andermann,1,2 * John J. Hopfield,3 andChristopher I. Moore4 1Program in Biophysics, Harvard University, Cambridge, Massachusetts 02138, 2Martinos Center, Massachusetts General Hospital-Nuclear Magnetic Resonance Center, Charlestown, Massachusetts 02129, 3Department of Molecular Biology, Princeton University, Princeton, New Jersey 08544, and 4McGovern Institute for Brain Research and Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Abstract
Top
Abstract
Introduction
We present evidence that resonance properties of rat vibrissae differentially amplify high-frequency and complex tactile signals. Consistent with a model of vibrissa mechanics, optical measurements of vibrissae revealed that their first mechanical resonance frequencies systematically varied from low (60-100 Hz) in longer, posterior vibrissae to high (750 Hz) in shorter, anterior vibrissae. Resonance amplification of tactile input was observed in vivo and ex vivo, and in a variety of boundary conditions that are likely to occur during perception, including stimulation of the vibrissa with moving complex natural stimuli such as sandpaper. Vibrissae were underdamped, allowing for sharp tuning to resonance frequencies. Vibrissa resonance constitutes a potentially useful mechanism for perception of high-frequency and complex tactile signals. Amplification of small amplitude signals by resonance could facilitate detection of stimuli that would otherwise fail to drive neural activity. The systematic map of frequency sensitivity across the face could facilitate texture discrimination through somatotopic encoding of frequency content. These findings suggest strong parallels between vibrissa tactile processing and auditory encoding, in which the cochlea also uses resonance to amplify low-amplitude signals and to generate a spatial map of frequency sensitivity.
Key words: vibrissa; whisker; somatosensory; resonance; rat; frequency
Introduction
Rats can use their posterior vibrissae (whiskers) as high-acuity sensors for detection and discrimination (Guic-Robles et al., 1989; Carvell and Simons, 1990
In many sensory systems, mechanical properties of peripheral sensors play an essential role in filtering information. Mechanical resonance, the propensity of a structure to demonstrate greater amplitude of vibration when stimulated at a specific frequency, is one key property used. Resonance is used in biological (e.g., the inner ear) and human-made (e.g., functional magnetic resonance imaging) sensing systems to enhance both detection and discrimination of signals. In detection, the tendency of a structure to vibrate at a larger amplitude when stimulated at a specific frequency facilitates the probability that the structure will be detected by a nervous system or sensing device. In discrimination, the variation in the specificity of resonance tuning of the sensors allows a sensing system to distinguish between the different frequencies that characterize distinct objects. In complex stimulus processing, a gradient in resonance tuning properties over an array of receptors enables the system to prepare the information for parallel processing, decomposing the signal into an ensemble of components at different frequencies. The cochlea is the primary example of a biological sensing system that employs the principle of resonance in these three contexts (Kiang et al., 1965
Here, we show that vibrisse resonance amplifies and bandpass filters tactile stimuli. In agreement with a biomechanical model of the vibrissa, optical recording of vibrissae revealed that they resonate across a range of biologically relevant stimulus conditions and demonstrate strong frequency tuning, and that resonance frequencies correlate with vibrissa length. As such, the anterior-posterior gradient of increasing vibrisse length on the rat face provides a systematic map of frequency sensitivity. These observations suggest that vibrissa resonance is optimally positioned to increase the range of detection and the specificity of discrimination, and may provide the ability to represent complex stimuli through a compact, somatotopically distributed code. The relevance of these biomechanical observations is highlighted by ongoing studies in our laboratory showing that vibrissa resonance is translated into neural activity (Andermann et al., 2002
Materials and Methods
All of the experiments were performed in compliance with research protocol guidelines approved by the Massachusetts General Hospital. Rats (n = 11) were anesthetized with urethane (1.4 gm/kg, i.p.) and placed in a stereotaxic frame (Kopf Instruments, Tujunga, CA) on a floating table (TMC) to minimize external vibrations and ensure maximal stability. All of the ex vivo vibrissa experiments were conducted on vibrissae carefully removed from the rat face after termination of the experiment.Vibrissa stimulation in PZ mode. Vibrissa measurements were performed under two conditions: (1) in vivo: vibrissa motion was measured while vibrissae were left intact on the face of a head-fixed, anesthetized rat, and (2) ex vivo: vibrissae were clamped to a stiff metal beam at 2 mm from their base. We used high-performance piezoelectric (PZ) bimorphs (Q234-H4CL-303X; Piezo Systems) that were customized to have a high fundamental resonance (
850 Hz; achieved by reducing piezoelectric length), calibrated with optoelectronics and compensating output voltage adjustment to <3% amplitude deviation from 5 to 600 Hz (Andermann et al., 2002
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Figure 2. Vibrissae resonate. The average amplitude of vibrissa motion in response to a periodic ex vivo PZ stimulation of a C3 vibrissa from the left side of the rat face at 5 Hz intervals, 5-600 Hz. C3 displays an 11-fold amplification when driven at its FRF of 385 Hz (gray bar). The vibrissa motion and the PZ motion, when driven by a periodic input at 320, 385, and 450 Hz, are shown in the insets. Note the increase in the amplitude and the 90° phase shift at the FRF. A similar phase shift (
Vibrissa stimulation in pulse mode. In in vivo and ex vivo conditions, the vibrissa was deflected manually with a solid rod and allowed to relax freely to rest. The vibrissa motion signal from the IR switch was acquired as described above, and local maxima and minima were located. Midpoints between these extrema were least-squares fit to the two-parameter function Be -t/
2, which was then subtracted from the data. The absolute values of the adjusted extrema were then fit to the two-parameter function Ae -t/
Measurement of vibrissa sweep past a complex texture. Periodic grating (50 pin cable; spatial frequency, 0.78/mm) or sandpaper (40 or 80 grit; Norton, Akron, OH; rms amplitudes of
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Figure 7. Complex textures evoke resonance in vibrissae. A, Experimental setup of the texture wheel driving vibrissa motion. Under natural conditions, rats may contact the stimulus at the tip, in the middle, or close to the base of the vibrissa (Brecht et al., 1997
Model of the vibrissa as a thin elastic beam. To establish specific predictions regarding vibrissa behavior, the following biomechanical model was developed. The thin elastic beam (TEB) was described with a single partial differential equation, by equating the shear and the bending moments (Den Hartog, 1952
where y(x) is the displacement of the vibrissa from its principal axis caused by bending, E is the bending modulus, I(x) is the moment of inertia, µ(x) is the linear density,
(1) is the damping coefficient, and f(x,t) is an external force applied to the tip of the vibrissa (f = 0 away from x = L) (see Fig. 1C) (Den Hartog, 1952
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Figure 1. A diagram of a TEB expressing resonance and the vibrissa sweeping past a surface. A, Left, When stimulated at frequencies lower than the FRF, TEB motion reflects the amplitude of displacement. Right, When driven at its FRF, a TEB demonstrates a significantly larger amplitude motion at its resonance mode. The increase in motion amplitude at this mode is accompanied by a 90° phase shift. Insets: gray, stimulus wave form; black, TEB motion. B, As the vibrissa sweeps past a surface, spatial frequency components in the surface exert a time-varying force on the vibrissa, causing it to deflect at specific temporal frequencies. As with the TEB motion in A, this action should induce resonance in the vibrissa. The vibrissa base is secured in the FSC. C, A diagram of the axes and directions of motion used in the model.
By the method of separation of variables (Weaver et al., 1990
n(x), which oscillate with corresponding characteristic frequencies,
n. The characteristic frequencies for a conical beam (the model that best approximates the shape and resonance behavior of vibrissae) (see Table 2) are given by:
where rbase is the radius at the base, L is the length,
(2) is the density of the vibrissae, and
n are constants encapsulating boundary conditions (see below) and the geometry of the vibrissa (Weaver et al., 1990
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Table 2. Vibrissa measurements
We considered the effect on the system when forcing was temporally periodic with frequency
. Decomposing over the spatial modes, the steady-state solution to the forced equation can be represented as follows:
The amplitude (Cn) of the oscillation of spatial mode (
(3) n) of the oscillation with respect to the driving force are given by the following (Weaver et al., 1990
(4) where A is the forcing amplitude. From Equation 4, the oscillation amplitude of a particular mode is greatest when the driving frequency is near the characteristic frequency (
(5) Boundary conditions describe the configuration in which external forces drive vibrissa motion and are critical to defining resonance behavior. We assumed for the purpose of this initial description that the vibrissa was clamped rigidly in the follicle at the base [y(0) = y'(0) = 0]. Vibrissa motion typically occurs in one of three boundary conditions. In a fixed-free boundary condition, the vibrissa is not in contact at the tip, as in whisking in air [y''(L) = y'''(L) = 0]. In a fixed-pinned boundary condition, the vibrissa tip is pushed against an object but not held rigidly, similar to the scanning behavior during texture perception [y(L) = y''(L) = 0]. In a fixed-fixed boundary condition, the vibrissa is rigidly attached at the tip [y(L) = y'(L) = 0] (Weaver et al., 1990
Fitting of the bending modulus. From the solution to Equation 2 for the fixed-free condition, the model predicted that the coefficient for the resonance frequency was
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Table 1. Vibrissa FRFs measured in four conditions from the left and right Crows
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Figure 3. Vibrissae are underdamped. A, Motion trace of a C3 vibrissae from the right side of the face after a pulse deflection ex vivo. The vibrissa undergoes several oscillations before relaxing to the original position. Gray, Vibrissa. Black, Fit to model. Inset, Equation to fit (see Materials and Methods). B, A plot of the damping coefficients versus 1/FRF of vibrissae as measured in pulse mode, in vivo and ex vivo. Circles, Experimental results. Line, Least-squares fit. Slope of line (C) = 1.3; R2 = 0.93.
Prediction of FRF by the model. The radius of the vibrissa was measured at the base, in the middle, and at the tip of the vibrissa using a stage micrometer at 40x magnification. We confirmed that the vibrissa could be described as conical in shape (Table 2), an approximation we used for the model. Equation 2 was used (see Fig. 6) to predict the resonance frequencies from geometrical measurements across all of the macrovibrissae on a second rat's face, using the E and
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Figure 6. The biomechanical model of the vibrissae reliably predicts their FRF across animals. A, Color map of the PZ-mode FRFs predicted by the model for vibrissae from one rat mystacial pad, using the measurements of their rbase and L. The FRFs (in Hz) are displayed in gray scale and in inset text. Each circle represents a single vibrissa. Arcs are denoted by numerals and rows by letters. Values used for
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Figure 5. Vibrissa FRF scales linearly as a function of its radius and length in PZ and pulse mode, in vivo and ex vivo. A, Plot of the FRFs measured in PZ mode from 10 C-row vibrissae in vivo (black circumference lines, open circles) and ex vivo (gray circumference lines, closed circles) versus the ratio of rbase/L2, as measured for the same vibrissae. Circles, Experimental values. Lines, Least-square fit. In vivo, C = 3.2 x 10 6 Hz · mm; R 2 = 0.96. Ex vivo, C = 3.5 x 10 6 Hz · mm; R 2 = 0.93. B, Plot of the FRFs measured in pulse mode from the same 10 vibrissae versus the ratio of rbase /L 2. In vivo, C = 1.7 x 10 6 Hz · mm; R 2 = 0.97. Ex vivo, C = 1.7 x 10 6 Hz · mm; R 2 = 0.94. C, Plot of the FRFs measured in PZ mode from 10 vibrissae versus FRFs measured in pulse mode (data from parts A and B combined). In vivo, C = 1.9, R2 = 0.98. Ex vivo, C = 1.9; R2 = 0.87.
Model of vibrissa sweep past a complex texture. The effect of the complex texture on the vibrissa was modeled by defining the force exerted on the vibrissa by the texture at varying velocities. A complex texture was defined, whose spatial amplitude spectrum is represented by P(u), the amplitude coefficient at spatial frequency u. When the vibrissa sweeps past this simulated texture at constant velocity v, the temporal frequency spectrum of the force exerted on the vibrissa can be represented as follows:Equation 6 allows for a one-to-one conversion between the spatial frequency spectra of textures and the temporal frequency spectrum of the force exerted on the vibrissa as a result of its motion. The force of the vibrissa can be discretized over the frequencies
(6) where Cn,k and
(7)
Results
We first describe the vibrissa model used to develop a set of quantitative predictions for vibrissa behavior and then discuss the testing of these predictions by optical monitoring of vibrissa motion.Description of the vibrissa as a TEB
The vibrissa is a thin, long, pliable hair, attached underneath the skin in a follicle-sinus complex (FSC) (Fig. 1B). As such, a reasonable first-order approximation of the vibrissa is a thin elastic beam—an object whose length is significantly greater than its width, that is of a uniform shape (conical or cylindrical), and that has intermediate boundary conditions. Elasticity theory shows that a TEB possesses characteristic spatial modes (patterns) of motion at progressively higher temporal frequencies (Landau and Lifshitz, 1970Model predictions and experimental verification
As described in Materials and Methods, we developed a biomechanical model of the vibrissa as a TEB and derived specific analytical predictions about its resonance behavior under a set of different boundary conditions. To experimentally test a set of five resonance-related predictions derived from Equations 2, 4, and 5, we drove the vibrissae at the two extremes of boundary conditions they are likely to encounter while contacting an object. At one end of the continuum, emulating a fixed-free condition, we provided transient sharp deflections of the vibrissa and measured its relaxation dynamics (the pulse mode). At the other end of possible boundary conditions, we fixed the vibrissa tip to a calibrated, high-resonance frequency piezoelectric bimorph (piezoelectric FRF, >850 Hz) (see Materials and Methods) and drove it across a range of frequencies from 0 to 600 or 750 Hz (the PZ mode) at tip deflections of
Prediction 1: vibrissae resonate
When stimulated at their FRFs, vibrissae should demonstrate significantly larger oscillations than at other stimulus frequencies, as in Equation 4. In PZ-driven oscillations, the amplitude of vibrissa motion often increased >10-fold as the driving frequency approached the FRF. Figure 2 depicts the relative amplitude of the frequency response of a C3 vibrissa to constant amplitude periodic PZ stimulation. The vibrissa demonstrated sharp tuning to within 20 Hz of the FRF of 375 Hz, resulting in up to an order of magnitude increase in its motion amplitude. The insets in Figure 2 display the relative amplitude of motion of the vibrissa and of the driving frequencies and the phase shift from the input oscillation at frequencies below the FRF, at the FRF, and above the FRF. Resonance amplification was observed in all of the vibrissae measured, spanning the first five arcs on the rat face (Greek arc - arc 4, n = 61 of 61 vibrissae; n = 8 rats).To fit the parameters of the model for various boundary conditions, we measured the resonance behavior in 10 vibrissae within a row in vivo (the
and C1-C4 from both sides of the face in one rat) with PZ and pulse stimulation and then plucked the vibrissae (postmortem) and repeated these measurements ex vivo (Table 1).
Prediction 2: vibrissae are underdamped and demonstrate sharp tuning curves
For resonance amplification to occur, vibrissae must be under-damped. Furthermore, the degree of tuning of the vibrissa resonance response (the sharpness of the peak) should be dependent on the degree of damping (Gelfand, 19982, of the peak amplitude) from PZ measurement. The Q values observed (mean = 9.8; SD = 3.6) (Table 1) were comparable with similar measurements made in bandpass-tuned neurons in the auditory pathway (Geisler, 1998
Prediction 3: a posterior-to-anterior gradient of frequency tuning exists across vibrissae
From the model, vibrissa FRFs were predicted to scale as the ratio of the radius at the base over length squared (Eq. 2). As vibrissae increase in length along the anterior-to-posterior axis, they should exhibit a systematic decrease in their FRFs along a row. For 10 C-row vibrissae measured in all four stimulation conditions (in vivo and ex vivo; PZ and pulse stimulation), this gradient in FRFs was present (Table 1). Figure 4A depicts the posterior-anterior shift in FRFs along a C row of vibrissae recorded during PZ stimulation. This systematic frequency gradient was subsequently confirmed by in vivo PZ measurements in 61 vibrissae. Within a row, FRFs increased from posterior to anterior vibrissae, whereas vibrissae within a single arc possessed similar FRFs (consistent with the similarity in vibrissa lengths within an arc) (Table 2, Fig. 4B). Figure 4 highlights a finding that was consistent across measurements—the similarity in expressed FRFs of the 1 and 2 arcs, resulting from their typically similar lengths (in Fig. 4A, the C1 and C2 vibrissa were both 41 mm long) (for sample vibrissa parameters from another animal, see also Fig. 6 and Table 2). The FRFs of the vibrissae presented in Table 1 scaled linearly with rbase/L2 (R2 = 0.95, 0.97) (Fig. 5A,B), allowing us to fit the values for E and
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Figure 4. A systematic anterior-posterior gradient of FRFs on the rat face. A, The average amplitude of vibrissa motion in response to bursts of PZ stimulation of the ex vivo
Prediction 4: resonance behavior is observed across varied boundary conditions
As predicted by the model, across all of the boundary conditions measured, FRFs were correlated with the length of the vibrissae (R2 = 0.97 and 0.96 in vivo and R2 = 0.94 and 0.93 ex vivo for pulse and PZ measurements, respectively) (Fig. 5), and the gradient of FRFs along a row was preserved for in vivo and ex vivo experimental conditions. Our various experimental configurations also confirmed the predicted importance of boundary conditions for resonance behavior. In pulse mode, the tip of the vibrissa was free, whereas the base was secured in the FSC, corresponding to the fixed-free boundary condition. In comparison, the tip of the vibrissa was more constrained in PZ mode, approximating the fixed-pinned or the fixed-fixed boundary condition. As predicted from Equation 2, the FRFs in PZ mode were higher than in pulse mode for the same vibrissae. To compare the dependence of FRF on the boundary conditions, we performed a least-square fit between the PZ- and the pulse-mode FRFs. We found that the ratio ofPrediction 5: vibrissa resonance is evoked by complex textures
Having studied resonance amplification under controlled conditions, we next sought to examine the contributions of resonance to vibrissa motion under more natural conditions, emulating realistic texture contact at typical whisking velocities. To develop predictions regarding the behavior of the vibrissa in this context, we modeled a vibrissa sweeping across a grating or a complex texture (e.g., sandpaper) at varying velocities (see Materials and Methods). For this simulation, the spatial frequency spectrum of the grating was chosen to have a single peak, whereas the complex texture was chosen to have three prominent peaks at three spatial frequencies and significantly smaller amplitudes at all of the other frequencies. In Figure 7, B and F, we plotted the predicted temporal frequency spectrum of vibrissa motion in response to stimulation by these textures at varying velocities. The temporal frequency of the vibrissa response is depicted on the y-axis, and the sweep velocity is depicted on the x-axis. The color code denotes the amplitude of the Fourier component of the response of the model vibrissa at a particular frequency. Three central predictions for the response of the vibrissa were generated by the model. At all of the velocities, horizontal bands of increased amplitude at the FRF of the vibrissa were apparent. This finding suggested that the vibrissa should be driven to vibrate at its FRF by any rough textured stimulus that contains some power at its FRF. The brighter diagonal bands corresponded to the effect of the spatial frequency peaks in the texture stimulus: with increased contact velocity, the same spatial frequency should drive the vibrissa at a higher temporal frequency (see Materials and Methods). The largest model vibrissa motions during stimulus contact occurred at the intersection of the horizontal and the diagonal bands. Here, the distinct spatial component was presented to the vibrissa at its FRF (v = u/w1). The model predicted that the greatest absolute amplification of vibrissa motion driven by a complex texture occurs if the texture possesses a prominent spatial frequency component that, for a given sweep velocity, drives the vibrissa at the FRF. It is important to note that, at natural whisking speeds (To test these predictions for vibrissa responses to complex stimuli, we presented a moving textured stimulus to in vivo vibrissae by leaning them against a rotating wheel covered with a periodic grating or sandpaper, and monitoring vibrissa motion while spinning the computer-controlled wheel at different velocities (Fig. 7A). The texture covered one-half of the circumference of the smooth, plastic wheel, enabling us to measure the response of the vibrissa to rough and smooth textures. As predicted by the model (Fig. 7B,F), the frequency spectrum of vibrissa motion during texture contact demonstrated a prominent peak at the FRF, independent of the velocity of the wheel (horizontal band of signal highlighted with a blue bar in C and G). This effect was less prominent for the periodic grating, which had less frequency content outside of its dominant periodic spatial frequency (Fig. 7C,D). As expected from the model, the spectrum of the vibrissa sweep past a periodic grating displayed a single prominent diagonal band of amplification (Fig. 7C, diagonal band in green). The ratio of the temporal frequency to velocity within that band (0.8 mm-1) corresponded to the measured spatial frequency of the grating (0.78 mm-1). Figure 7E shows the trace of vibrissa motion past the grating, in which the amplification of the fundamental mode at the FRF of the vibrissa is apparent. This amplification was 10 times greater when the velocity of the grating motion created a temporal driving frequency that coincided with the FRF of the vibrissa.
The spectrum of motion of the vibrissa during sandpaper contact also revealed several peaks corresponding to the peaks in the spatial spectrum of the sandpaper (Fig. 7F,G, diagonal band highlighted in green). When the wheel rotated at the velocity at which the dominant spatial frequency of sandpaper is encountered at the FRF of the vibrissa, the amplitude at the resonance frequency of vibrissa motion again was increased by a factor of 3-5 (Fig. 7G,H). Figure 7, D and H, demonstrates that the vibrissae responded to the rough stimuli by increasing their amplitude of motion in response to the spatial components in the texture, compared with the response to a smooth stimulus. The amplification of vibrissa motion at the FRF (at frequencies between
Utility of resonance for detection and discrimination
Resonance behavior allows for up to an order of magnitude amplification of motion in the vibrissa with respect to the amplitude of the driving oscillations. Because vibrissae, as an ensemble, span a large range of frequencies, resonance endows the vibrissa system with an ability to amplify a wide range of textures, thus increasing the detection capabilities of the system (Fig. 8A). Rats are known to vary their whisk velocity during texture-grating exploration (Carvell and Simons, 1990
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Figure 8. Models of vibrissae resonance in detection and discrimination. A, An idealized diagram of the spectra of vibrissae within a single row. As an ensemble, vibrissae should amplify all of the high-frequency stimuli from 50 to 700 Hz. As such, they may improve the detection of small-amplitude, high-frequency stimuli that otherwise would not drive sufficient vibrissa motion to recruit significant changes in neural activity. B, A diagram of the response of a single versus a pair of vibrissae with overlapping frequency spectra to two sinusoidal stimuli. The two stimuli are presented at frequencies f1 and f2, which are equidistant from the FRF (
Vibrissa resonance may also facilitate discrimination of different spatial textures. The neural code for discrimination of the spatial frequency of a given surface could consist of a relative comparison of the mean firing rates between arcs of vibrissae, where the more posterior arc vibrissae will amplify signals with lower spatial frequency components (Fig. 8). In our experiments, a significant peak was detected in the power spectrum of a vibrissa at its FRF when it was driven by sandpaper presented at differing velocities. This result demonstrated that even complex, natural stimuli excite the fundamental resonance mode of a vibrissa, and thus texture identification could be facilitated by the vibrissae resonance properties. Figure 8B shows a diagram of the proposed discrimination mechanism. A single vibrissa tuned to the frequency w1 can experience similar resonance amplification when driven at two different frequencies, f1 and f2 (f1 < w1 < f2). However, the addition of another vibrissa with an elevated resonance frequency w2 will result in a differential response motion in the two vibrissae. Subsequently, the relative neural response in a given somatotopic vibrissa location can be assayed, and the two surfaces can be discriminated from each other (Fig. 8B).
Discussion
In this study, we provide evidence for a novel mechanism of tactile sensory encoding, in which vibrissa resonance properties selectively amplify high-frequency signals. We found that vibrissae exhibit resonance amplification under conditions that span those generated during surface exploration. Such natural stimuli include free vibrissa oscillations after punctate contact and vibrissa resonance during continuous high-frequency interactions with complex surfaces. The range of FRFs spanned 50-750 Hz for the macrovibrissae, and was organized in a systematic posterior-anterior gradient along vibrissa rows. Within vibrissa arcs, FRFs were similar because of the consistency in their geometry. These findings suggest that, as the name "vibrissa" implies, mechanical resonance driven by vibration is important to the neural representation of surface textures in the vibrissa-to-barrel pathway. This suggestion is supported by trigeminal and cortical recordings using identical stimuli in our laboratory (Andermann et al., 2002Vibrissa resonance and psychophysical capabilities of rats
The proposed roles of vibrissa resonance in detection and discrimination (Fig. 8) are consistent with the known psychophysical capabilities in rats. Detecting differences between smooth and rough surfaces is possible with a single vibrissa (Carvell and Simons, 1990We emphasize that, in the proposed framework, texture discriminations made with the vibrissa system can be represented as relative neural activity comparisons between arc signals. These relative judgements do not require that the rat know the temporal frequency generated by a given velocity convolved with a spatial frequency—a difficult decoding problem for a variety of reasons, including continued vibrissa growth (Ibrahim and Wright, 1982
Vibrissa resonance and the representation of complex surfaces
We showed that vibrissae can amplify the periodic components in a complex texture. This finding suggests that, when the vibrissae, as an ensemble, sweep past a complex texture, the amplitude of motion of each vibrissa will be proportional to the coefficient of the frequency component in the force exerted on the vibrissae at its resonance frequency. The spectral content of surface features of many natural textures, such as concrete and sandpaper, is known to have maximal power between 0.01 and 0.5 mm (Costa, 2000Parallels with the auditory system and neural implications
The system we described for tactile sensory amplification is similar to known mechanisms in the auditory system. In auditory processing, several resonance properties of the cochlea create a spatial gradient of temporal frequency responses, much like the spatial gradient observed here across the rat face (Geisler, 1998The parallels between the model proposed here and the auditory system suggest that vibrissa resonance may also act to amplify signals that are carried in media other than hard surfaces (e.g., sound pressure waves in air). In support of this view, cercal hairs of invertebrates show distinct sensitivity to the frequency composition of air currents, potentially using similar mechanisms (Levin and Miller, 1996
Future directions
An important future direction for studies of resonance will be to elucidate the effects that vibrissa bending and contact point have on resonance amplification. The effective boundary condition at the end of a vibrissa sweeping across a rough surface depends on the details of contact. For strong contact forces and rough surfaces, the vibrissa may jump (in a stick-slip manner) between pinning points representing a pinned-end condition. For weak contacts, texture probably provides a spatially varying coefficient of sliding friction, and the motion of the whisker should reflect the spatial Fourier coefficients of texture. Although no studies have examined resonance behavior in the awake behaving rat whisking over a texture, Hartmann et al. (2003Under the currently examined conditions, higher resonance frequencies, above the FRF, were observed in many vibrissae (e.g., the second amplification region at 410 Hz in the
A caveat regarding the model proposed here is that the predictions generated from it are constrained to the linear regime, valid for vibrissa deflections of up to 1 mm. Preliminary experiments suggest that this assumption is well met (Andermann and Moore, unpublished observations). The principle of resonance amplification should be preserved by larger deflections that may be used in other whisking contexts, although this assumption needs to be tested empirically.
Vibrissa damping could also significantly influence the expression of resonance effects, as was evident from our model and measurements. As suggested by Yohro (1977
Footnotes
Received Mar 14, 2003; revised May 12, 2003; accepted May 13, 2003.* M.A.N. and M.L.A. contributed equally to this study.
This work was supported by the Howard Hughes Medical Institute, the National Institutes of Health, and the McDonnell-Pew Foundation. We thank Mitra Hartmann, Jason Ritt, Catherine Garabedian, and Lisa Shatz for helpful comments and discussions, Andy Siegel for assistance in developing optical monitoring, David Boas and the Martinos Center for generous provision of equipment and resources, and Ram Ramaprasad and TRI/Princeton for providing equipment for vibrissa measurements.
Correspondence should be addressed to Dr. Christopher I. Moore, E25-436, McGovern Institute and Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139. E-mail: cim{at}ai.mit.edu.
Copyright © 2003 Society for Neuroscience 0270-6474/03/236499-11$15.00/0
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